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Marathon Runner

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Question

A marathon runner only runs in windy weather conditions. Magically, the wind in his area is always the same speed, but can have different directions. He knows he can run a marathon in $n$ hours if the wind blows against him. Conversely, he can run a marathon in $m < n$ hours if the wind blows in his direction. How long would it take the runner to complete a marathon in non-windy weather conditions? Provide your answer when $n=20/3$ and $m=4$.

Practice focus

This Brainteasers problem is tagged Brainteasers. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.

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